The data set below on the left represents the annual rate of return (in percent)
ID: 3063575 • Letter: T
Question
The data set below on the left represents the annual rate of return (in percent) of eight randomly sampled bond mutual funds, and the data set below on the right represents the annual rate of return (in percent) of eight randomly sampled stock mutual funds. Use the information in the table below to complete parts (a) through (d). Then complete part (a) Determine the mean and standard deviation of each data set. The mean of the data set for bond mutual funds is 2.575 (Type an integer or decimal rounded to three decimal places as needed.) The standard deviation of the data set for bond mutual funds is 0.669 Bond mutual funds 3.4 2.0 2.1 3.6 2.6 29 1.8 2.2 Stock mutual funds 9.6 7.8 9.3 7.6 8.6 74 8.3 7.1 Type an integer or decimal rounded to three decimal places as needed.) The mean of the data set for stock mutual funds is 8.213 Type an integer or decimal rounded to three decimal places as needed.) The standard deviation of the data set for stock mutual funds is 0.903 (Type an integer or decimal rounded to three decimal places as needed.) (b) Based only on the standard deviation, stock mutual funds have more spread (c) What proportion of the bond mutual funds are within one standard deviation of the mean? 68.3% Type an integer or decimal rounded to three decimal places as needed.) What proportion of the stock mutual funds are within one standard deviation of the mean? (Type an integer or decimal rounded to three decimal places as needed.) (d) The coefficient of variation, CV, is defined as the ratio of the standard deviation to the mean of a data set.Explanation / Answer
All your entered answers are correct. Rest of the answers with explanations are given below.
The proportion of the bond mutual funds are within one standard deviation of mean.
By empirical rule, the answer is 68.3% = 0.683
The proportion of the stock mutual funds are within one standard deviation of mean.
By empirical rule, the answer is 68.3% = 0.683
(d)
The CV of the dataset for bond mutual funds = Standard deviation / mean = 0.669 / 2.575 = 0.260
The CV of the dataset for stock mutual funds = Standard deviation / mean = 0.903 / 8.213 = 0.110
As, CV for bond mutual funds is greater than CV for stock mutual funds
Based on the coefficient of variation, bonds mutual funds have more spread.
(e)
Height in inches = 65, 65, 72, 75, 74, 66, 68, 68
Height in cms = 165.1, 165.1, 182.88, 190.5, 187.96, 167.64, 172.72, 172.72
Mean of dataset of height in inches = 69.125
Standard deviation of dataset of height in inches = 4.016
Mean of dataset of height in centimeters = 175.578
Standard deviation of dataset of height in centimeters = 10.200
Based on the standard deviation, dataset for height in centimeters have more spread.
CV of the dataset for height in inches = 4.016 / 69.125 = 0.058
CV of the dataset for height in centimeters = 10.200 / 175.578 = 0.058
As, CV of the dataset for height in inches is equal to CV of the dataset for height in centimeters, the correct option is,
D. When converting units of measure, the coefficient of variation is unchanged.
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